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If ∠7+∠6=180°m∠7+m∠6=180° which Theorem would prove the lines are parallel.

If ∠7+∠6=180°m∠7+m∠6=180° which Theorem would prove the lines are parallel.-example-1
User AitorF
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1 Answer

3 votes

Step-by-step explanation:

The Same Side interior angles Theorem states that if two lines are parallel then the angles on the same side of the transversal are supplementary (which means they add up to 180°).

The Converse of the Same Side interior angles Theorem states that if the interior angles on the same side of the transversal ( a fancy name for the intersecting line) are supplementary ( means they add up to 180°), then the two lines are parrallel.

Now in our case, angles 6 and 7 are the interior angles. Moreover, angles 6 and 7 lie on the same side of the transversal line and ∠6 + ∠7 = 180° ( meaning they are supplementary). Therefore, by the converse of the Same Side interior angles Theorem, the two lines are parrallel.

Answer:

d. Converse of the Same Side interior angles Theorem.

If ∠7+∠6=180°m∠7+m∠6=180° which Theorem would prove the lines are parallel.-example-1
User Jlconlin
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5.4k points
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